






"""simple docstring"""





from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
_SCREAMING_SNAKE_CASE   :							List[Any]          =		200
# Number of elements selected in every generation of evolution. The selection takes
# place from best to worst of that generation and must be smaller than N_POPULATION.
_SCREAMING_SNAKE_CASE   :							Tuple          =		50
# Probability that an element of a generation can mutate, changing one of its genes.
# This will guarantee that all genes will be used during evolution.
_SCREAMING_SNAKE_CASE   :							Dict          =		0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 1000))







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						str					) ->							tuple[str, float]:
  lowerCamelCase_       	=		len([g for position, g in enumerate(_lowerCamelCase					) if g == main_target[position]]					)
  return (item, float(_lowerCamelCase					))







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						str					) ->							tuple[str, str]:
  lowerCamelCase_       	=		random.randint(0						,							len(_lowerCamelCase					) - 1					)
  lowerCamelCase_       	=		parent_a[:random_slice] + parent_a[random_slice:]
  lowerCamelCase_       	=		parent_a[:random_slice] + parent_a[random_slice:]
  return (child_a, child_a)







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						list[str]					) ->							str:
  lowerCamelCase_       	=		list(_lowerCamelCase					)
  if random.uniform(0						,							1					) < MUTATION_PROBABILITY:
    lowerCamelCase_       	=		random.choice(_lowerCamelCase					)
  return "".join(_lowerCamelCase					)







def 	lowerCamelCase__			(				_lowerCamelCase			:						tuple[str, float]						,							_lowerCamelCase			:						list[tuple[str, float]]						,							_lowerCamelCase			:						list[str]						,							) ->							list[str]:
  lowerCamelCase_       	=		[]
  # Generate more children proportionally to the fitness score.
  lowerCamelCase_       	=		int(parent_a[1] * 100					) + 1
  lowerCamelCase_       	=		10 if child_n >= 10 else child_n
  for _ in range(_lowerCamelCase					):
    lowerCamelCase_       	=		population_score[random.randint(0						,							_lowerCamelCase					)][0]

    lowerCamelCase_	,      lowerCamelCase_       	=		crossover(parent_a[0]						,							_lowerCamelCase					)
    # Append new string to the population list.
    pop.append(mutate(_lowerCamelCase						,							_lowerCamelCase					)					)
    pop.append(mutate(_lowerCamelCase						,							_lowerCamelCase					)					)
  return pop







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						list[str]						,							_lowerCamelCase			:						bool = True					) ->							tuple[int, int, str]:

  # Verify if N_POPULATION is bigger than N_SELECTED
  if N_POPULATION < N_SELECTED:
    lowerCamelCase_       	=		F'''{N_POPULATION} must be bigger than {N_SELECTED}'''
    raise ValueError(_lowerCamelCase					)
  # Verify that the target contains no genes besides the ones inside genes variable.
  lowerCamelCase_       	=		sorted({c for c in target if c not in genes}					)
  if not_in_genes_list:
    lowerCamelCase_       	=		F'''{not_in_genes_list} is not in genes list, evolution cannot converge'''
    raise ValueError(_lowerCamelCase					)

  # Generate random starting population.
  lowerCamelCase_       	=		[]
  for _ in range(_lowerCamelCase					):
    population.append(''.join([random.choice(_lowerCamelCase					) for i in range(len(_lowerCamelCase					)					)]					)					)

  # Just some logs to know what the algorithms is doing.
  lowerCamelCase_	,      lowerCamelCase_       	=		0, 0

  # This loop will end when we find a perfect match for our target.
  while True:
    generation += 1
    total_population += len(_lowerCamelCase					)

    # Random population created. Now it's time to evaluate.

    # Adding a bit of concurrency can make everything faster,
    #
    # import concurrent.futures
    # population_score: list[tuple[str, float]] = []
    # with concurrent.futures.ThreadPoolExecutor(
    #                                   max_workers=NUM_WORKERS) as executor:
    #     futures = {executor.submit(evaluate, item) for item in population}
    #     concurrent.futures.wait(futures)
    #     population_score = [item.result() for item in futures]
    #
    # but with a simple algorithm like this, it will probably be slower.
    # We just need to call evaluate for every item inside the population.
    lowerCamelCase_       	=		[evaluate(_lowerCamelCase						,							_lowerCamelCase					) for item in population]

    # Check if there is a matching evolution.
    lowerCamelCase_       	=		sorted(_lowerCamelCase						,							key=lambda _lowerCamelCase					: x[1]						,							reverse=_lowerCamelCase					)
    if population_score[0][0] == target:
      return (generation, total_population, population_score[0][0])

    # Print the best result every 10 generation.
    # Just to know that the algorithm is working.
    if debug and generation % 10 == 0:
      print(
          F'''\nGeneration: {generation}'''
          F'''\nTotal Population:{total_population}'''
          F'''\nBest score: {population_score[0][1]}'''
          F'''\nBest string: {population_score[0][0]}'''					)

    # Flush the old population, keeping some of the best evolutions.
    # Keeping this avoid regression of evolution.
    lowerCamelCase_       	=		population[: int(N_POPULATION / 3					)]
    population.clear()
    population.extend(_lowerCamelCase					)
    # Normalize population score to be between 0 and 1.
    lowerCamelCase_       	=		[
        (item, score / len(_lowerCamelCase					)) for item, score in population_score
    ]

    # This is selection
    for i in range(_lowerCamelCase					):
      population.extend(select(population_score[int(_lowerCamelCase					)]						,							_lowerCamelCase						,							_lowerCamelCase					)					)
      # Check if the population has already reached the maximum value and if so,
      # break the cycle.  If this check is disabled, the algorithm will take
      # forever to compute large strings, but will also calculate small strings in
      # a far fewer generations.
      if len(_lowerCamelCase					) > N_POPULATION:
        break


if __name__ == "__main__":
  _SCREAMING_SNAKE_CASE   :							Any          =		(
      '''This is a genetic algorithm to evaluate, combine, evolve, and mutate a string!'''
  )
  _SCREAMING_SNAKE_CASE   :							Optional[int]          =		list(
      ''' ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm'''
      '''nopqrstuvwxyz.,;!?+-*#@^\'èéòà€ù=)(&%$£/\\'''
  )
  _SCREAMING_SNAKE_CASE       ,				_SCREAMING_SNAKE_CASE       ,				_SCREAMING_SNAKE_CASE   :							str          =		basic(target_str, genes_list)
  print(
      F'''\nGeneration: {generation}\nTotal Population: {population}\nTarget: {target}'''
  )












"""simple docstring"""





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						complex						,							_lowerCamelCase			:						str = "x"						,							_lowerCamelCase			:						float = 10**-10						,							_lowerCamelCase			:						int = 1						,							) ->							complex:
  lowerCamelCase_       	=		symbols(_lowerCamelCase					)
  lowerCamelCase_       	=		lambdify(_lowerCamelCase						,							_lowerCamelCase					)
  lowerCamelCase_       	=		lambdify(_lowerCamelCase						,							diff(_lowerCamelCase						,							_lowerCamelCase					)					)

  lowerCamelCase_       	=		starting_point

  while True:
    if diff_function(_lowerCamelCase					) != 0:
      lowerCamelCase_       	=		prev_guess - multiplicity * func(_lowerCamelCase					) / diff_function(
          _lowerCamelCase					)
    else:
      raise ZeroDivisionError('Could not find root'					) from None

    # Precision is checked by comparing the difference of consecutive guesses
    if abs(next_guess - prev_guess					) < precision:
      return next_guess

    lowerCamelCase_       	=		next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(F'''The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}''')

  # Find root of polynomial
  # Find fourth Root of 5
  print(F'''The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}''')

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      F'''{newton_raphson('log(y) - 1', 2, variable='y')}''',
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      F'''{newton_raphson('exp(x) - 1', 10, precision=0.005)}''',
  )

  # Find root of cos(x)
  print(F'''The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}''')




